One of the things that tends to happen is that yes, they cut services. Often they cut services WITHOUT cutting spending--the point being to try to coerce the taxpayers into agreeing to tax increases--as a result of which the deficits actually increase, and the city starts defaulting on MORE payments.
Often municipal employees will continue showing up for work in hopes of getting paid some day.
The article states that bankruptcy for municipal entities is a messy business. And one small municipality has been put into "receivership" meaning that the courts have assigned an outside party to take over the situation. I would guess that higher-ranking creditors get paid, from sales of municipal assets, while low-ranking creditors get stiffed.